Problem: What number could replace $k$ below? $\dfrac{1}{2} = \dfrac{k}{4}$
Solution: The fraction on the left represents 1 out of 2 slices of a rectangular pie. What if we cut the pie into 4 slices instead? How many slices would result in the same amount of pie? We would need 2 slices. $\dfrac{1}{2} = \dfrac{2}{4}$ and so the answer is $2$ Another way to get the answer is to multiply by $\dfrac{2}{2}$ $\dfrac{2}{2} = \dfrac{1}{1} = 1$ so really we are multiplying by 1. The final equation is: $\dfrac{1}{2} \times \dfrac{2}{2} = \dfrac{2}{4} $ so our answer is $2$.